square of x+3/y+3z

asked by guest
on Apr 04, 2025 at 2:32 pm



You asked:

Evaluate the expression: (x+3y+3z)2{\left( x + \frac{3}{y} + 3 z \right)}^{2}

MathBot Answer:

Evaluated



(x+3y+3z)2=(x+3z+3y)2\displaystyle {\left( x + \frac{3}{y} + 3 z \right)}^{2} = \left(x + 3 z + \frac{3}{y}\right)^{2}

Expanded

(x+3y+3z)2=x2+6xz+6xy+9z2+18zy+9y2{\left( x + \frac{3}{y} + 3 z \right)}^{2} = x^{2} + 6 x z + \frac{6 x}{y} + 9 z^{2} + \frac{18 z}{y} + \frac{9}{y^{2}}

Factored

(x+3y+3z)2=(xy+3yz+3)2y2{\left( x + \frac{3}{y} + 3 z \right)}^{2} = \frac{\left(x y + 3 y z + 3\right)^{2}}{y^{2}}

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